4.3 Arithmetic Operators and Mathematical Functions Four basic operators: addition: + subtraction: - multiplication: * division: / Parentheses control the order of subexpression computation: (a + b) / 2 Multiplication and division bind more strongly than addition and subtraction: Big Java by Cay Horstmann Copyright © 2009 by John Wiley & Sons. All rights reserved.

Increment and Decrement items++ is the same as items = items + 1 items-- subtracts 1 from items Big Java by Cay Horstmann Copyright © 2009 by John Wiley & Sons. All rights reserved.

/ is the division operator Integer Division / is the division operator If both arguments are integers, the result is an integer. The remainder is discarded 7.0 / 4 yields 1.75 7 / 4 yields 1 Get the remainder with % (pronounced “modulo”) 7 % 4 is 3 Big Java by Cay Horstmann Copyright © 2009 by John Wiley & Sons. All rights reserved.

Example: Integer Division final int PENNIES_PER_NICKEL = 5; final int PENNIES_PER_DIME = 10; final int PENNIES_PER_QUARTER = 25; final int PENNIES_PER_DOLLAR = 100; // Compute total value in pennies int total = dollars * PENNIES_PER_DOLLAR + quarters * PENNIES_PER_QUARTER + nickels * PENNIES_PER_NICKEL + dimes * PENNIES_PER_DIME + pennies; // Use integer division to convert to dollars, cents int dollars = total / PENNIES_PER_DOLLAR; int cents = total % PENNIES_PER_DOLLAR; Big Java by Cay Horstmann Copyright © 2009 by John Wiley & Sons. All rights reserved.

To compute xn, you write Math.pow(x, n) Powers and Roots Math class: contains methods sqrt and pow to compute square roots and powers To compute xn, you write Math.pow(x, n) However, to compute x2 it is significantly more efficient simply to compute x * x To take the square root of a number, use Math.sqrt; for example, Math.sqrt(x) In Java,                        can be represented as (-b + Math.sqrt(b * b - 4 * a * c)) / (2 * a) Big Java by Cay Horstmann Copyright © 2009 by John Wiley & Sons. All rights reserved.

Analyzing an Expression Big Java by Cay Horstmann Copyright © 2009 by John Wiley & Sons. All rights reserved.

Mathematical Methods Function Returns square root power xy ex Math.sqrt(x) square root Math.pow(x, y) power xy Math.exp(x) ex Math.log(x) natural log Math.sin(x), Math.cos(x), Math.tan(x) sine, cosine, tangent (x in radians) Math.round(x) closest integer to x Math.min(x, y), Math.max(x, y) minimum, maximum Big Java by Cay Horstmann Copyright © 2009 by John Wiley & Sons. All rights reserved.

Cast converts a value to a different type: Cast and Round Cast converts a value to a different type: double balance = total + tax; int dollars = (int) balance; Math.round converts a floating-point number to nearest integer: long rounded = Math.round(balance); // if balance is 13.75, then rounded is set to 14 Big Java by Cay Horstmann Copyright © 2009 by John Wiley & Sons. All rights reserved.

Syntax 4.2 Cast Big Java by Cay Horstmann Copyright © 2009 by John Wiley & Sons. All rights reserved.

Arithmetic Expressions Big Java by Cay Horstmann Copyright © 2009 by John Wiley & Sons. All rights reserved.

Self Check 4.6 What is the value of n after the following sequence of statements? n--; n++; Answer: One less than it was before.

Self Check 4.7 What is the value of 1729 / 100? Of 1729 % 100? Answer: 17 and 29

Self Check 4.8 Why doesn’t the following statement compute the average of s1, s2, and s3? double average = s1 + s2 + s3 / 3; // Error Answer: Only s3 is divided by 3. To get the correct result, use parentheses. Moreover, if s1, s2, and s3 are integers, you must divide by 3.0 to avoid integer division: (s1 + s2 + s3) / 3.0

Self Check 4.9 What is the value of Math.sqrt(Math.pow(x,  2)  + Math.pow(y, 2)) in mathematical notation? Answer:              

Self Check 4.10 When does the cast (long) x yield a different result from the call Math.round(x)? Answer: cast does NOT round, simply truncates the decimal. There will be a difference when the fractional part of x is ≥ 0.5

Self Check 4.11 How do you round the double value x to the nearest int value, assuming that you know that it is less than 2 ·109? Answer: By using a cast: (int) Math.round(x)